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Some of the finite structures considered in graph theory have names, sometimes inspired by the graph's topology, and sometimes after their discoverer. A famous example is the Petersen graph, a concrete graph on 10 vertices that appears as a minimal example or counterexample in many different contexts. A labeled graph with 6 vertices and 7 edges. ...
The Petersen graph Another drawing of the Petersen graph, with only two crossings Another drawing, with each edge the same length The Petersen graph is a small graph that serves as a useful example and counterexample in graph theory. ...
Individual graphs
Triangle, K3, C3
n = 3, m = 3 In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ...
| Square, C4
n = 4, m = 4 In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ...
| Claw, K1,3, S4
n = 4, m = 4 In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set. ...
| Pentagon
n = 5, m = 5 In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ...
| Thomsen graph, Utility graph, K3,3
n = 6, m = 9 Image File history File links Complete_bipartite_graph_K3,3. ...
| Fano plane Image:Fano. ...
A finite geometry is any geometric system that has only a finite number of points. ...
| Cube
n = 8 In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ...
| | | | | Dodecahedron
n = ?, m = ? | Flower snark In graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to four. ...
| | | | Levi graph, Tutte eight-cage Image File history File links Tutte_eight_cage. ...
| Heawood graph Image File history File links Heawood_graph. ...
| Petersen graph Image File history File links Petersen_graph. ...
The Petersen graph Another drawing of the Petersen graph, with only two crossings Another drawing, with each edge the same length The Petersen graph is a small graph that serves as a useful example and counterexample in graph theory. ...
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Graph families
Complete graphs The complete graph on n vertices is often called the n-clique and usually denoted Kn, from German komplett. [citation needed] In the mathematical field of graph theory a complete graph is a simple graph where an edge connects every pair of vertices. ...
| | | | K4 Image File history File links Complete_graph_K4. ...
| K5 Image File history File links Complete_graph_K5. ...
| K6 Image File history File links Complete_graph_K6. ...
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Complete bipartite graphs The complete bipartite graph is ususally denoted Kn,m In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set. ...
K3,1 Image File history File links Complete_bipartite_graph_K3,1. ...
| K3,2 Image File history File links Complete_bipartite_graph_K3,2. ...
| K3,3 Image File history File links Complete_bipartite_graph_K3,3. ...
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Cycles The cycle graph on n vertices is called the n-cycle and usually denoted Cn. It is also called a cyclic graph, a polygon or the n-gon. Special cases are the triangle C3, the square C4, and the pentagon C5. In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ...
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